Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}5x-3y &= -7 \\ 5x+3y &= -4\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $10x = -11$ Divide both sides by $10$ and reduce as necessary. $x = -\dfrac{11}{10}$ Substitute $-\dfrac{11}{10}$ for $x$ in the top equation. $5( -\dfrac{11}{10})-3y = -7$ $-\dfrac{11}{2}-3y = -7$ $-3y = -\dfrac{3}{2}$ $y = \dfrac{1}{2}$ The solution is $\enspace x = -\dfrac{11}{10}, \enspace y = \dfrac{1}{2}$.